Question

let f be the function defined above, where c and d are constants. if f is differentiable at x = 2 what is the value of c + d?

Answer 1

Answer: The values for the constants are c=2, and d=-4.

explanation: We have the function f, defined as:

and

where c and d are constants.

So, if f is differentiable at x=2, then it must be continuos at x=2, therefore

Let's call this, equation 1.

On the other hand, we have that f is differentiable, therefore

and

so, we calculate

which, replacing in equation 1, gives us

Finally, the answer is that c=2, and d=-4.